6.3 Solving Systems of Equations by Elimination

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean to solve a system of equations by elimination?

Back

It means to eliminate one variable by adding or subtracting the equations, allowing you to solve for the other variable.

Front

What is the elimination method?

Back

A method for solving systems of equations by removing one variable, making it easier to solve for the other.

Front

How do you make the coefficients of x or y opposites in elimination?

Back

Multiply one or both equations by a number so that the coefficients of one variable are opposites.

Front

Solve by elimination: 2x + 3y = 6 and 4x + 6y = 12.

Back

No solution (the equations are dependent).

Front

Solve by elimination: 3x + 2y = 12 and 3x - 4y = 6.

Back

(2, 3) - the solution to the system.

Front

What is a dependent system of equations?

Back

A system where the equations represent the same line, resulting in infinitely many solutions.

Front

What is an independent system of equations?

Back

A system where the equations represent different lines, resulting in exactly one solution.

Front

What is an inconsistent system of equations?

Back

A system where the equations represent parallel lines, resulting in no solution.

Front

Solve by elimination: 5x + 2y = 10 and 5x - 3y = 5.

Back

(1, 2) - the solution to the system.